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Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond

Covers extensions of Buchberger's Theory and Algorithm, and promising recent alternatives to Gröbner bases.

Teo Mora (Author)

9781107109636, Cambridge University Press

Hardback, published 1 April 2016

834 pages, 40 b/w illus.
24 x 16.3 x 5.7 cm, 1.47 kg

In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.

Part VII. Beyond: 46. Zacharias
47. Bergman
48. Ufnarovski
49. Weispfenning
50. Spear2
51. Weispfenning II
52. Sweedler
53. Hironaka
54. Hironaka II
55. Janet
56. Macaulay V
57. Gerdt and Faugère
Bibliography
Index.

Subject Areas: Maths for computer scientists [UYAM], Number theory [PBH], Algebra [PBF], Mathematics [PB]

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